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Describe about Arithmetic and Geometric Series?
When the terms of a sequence are added together instead of separated by commas, the sequence becomes a series. You will use series in higher mathematics. Example 1: 3 + 6 + 9 + 12 + ...The pattern is add three to the previous term. When the pattern is to always add or subtract the same number, you have an arithmetic series. Example 2:1 + 2 + 4 + 8 + ...The pattern is multiply two to the previous term. A series that has a pattern of multiplying or dividing by the same number is called a geometric series.
1. a) Given a digraph G = (V,E), prove that if we add a constant k to the length of every arc coming out from the root node r, the shortest path tree remains the same. Do this by
If e were rational, then e = n/m for some positive integers m, n. So then 1/e = m/n. But the series expansion for 1/e is 1/e = 1 - 1/1! + 1/2! - 1/3! + ... Call the first n v
1/a+b+x =1/a+1/b+1/x a+b ≠ 0 Ans: 1/a+b+x =1/a+1/b+1/x => 1/a+b+x -1/x = +1/a +1/b ⇒ x - ( a + b + x )/ x ( a + b + x ) = + a + b/ ab ⇒
A function is an equation for which any x which can be plugged into the equation will yield accurately one y out of the equation. There it is. i.e. the definition of functions w
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Quadric Surfaces Earlier we have looked at lines and planes in three dimensions (or R 3 ) and when these are used fairly heavily at times in a Calculus class there are several
From a window x meters high above the ground in a street, the angles of elevation and depression of the top and the foot of the other house on the opposite side of the street are
State the following statement as a disjunction (in DNF) as well using quantifiers: There does not exit a woman who has taken a flight on each airline in the world.
prove same homotopy type is an equivalent relation
principal=2000 rate=5% time=2 years find compound interest
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